* King's appearance helps assuage worries about his health
* Stability of the world's largest oil exporter is global concern
Saudi King Abdullah has appeared on state television on Wednesday for the first time since his 11-hour operation to tighten a back ligament on Nov. 17, helping assuage fears over his health.
In footage broadcast on state television, the monarch, who is in his late 80s, appeared to be in good health as he sat in a chair receiving members of the royal family and officials at the National Guard's King Abdulaziz Medical City in the capital Riyadh.
Saudi stability is of global concern. The pivotal Gulf U.S. ally holds more than a fifth of world petroleum reserves and is the birthplace of Islam, where millions of Muslims flock to perform the annual haj pilgrimage.
"It should put to rest all the rumours that were circulated by unknown people," Jamal Khashoggi, an influential Saudi commentator said after footage of the king appeared on television.
"He looked okay for his age," he added.
Saudi media did not say when the king was expected to leave hospital.
Because power in the world's top oil-exporting country is concentrated in the hands of the king and top princes, their health is closely watched.
Rumours that the king's recovery was not going well circulated over social media networks sending the index to a 10-month low on Tuesday.The market rose 1.1 percent on Wednesday.
Top Saudi royals have repeatedly visited the king in hospital since the royal court announced the surgery in his upper back on Nov. 18 a success, according to state media.
Saudi analysts have said it was understandable that recovery would take time, given the king's advanced age.
Saudi state media have been reporting visits by members of the royal family and senior officials to the hospital and Crown Prince Salman has twice come out to reassure Saudis about the king's health. But the lack of pictures of the monarch has only fuelled social media speculation about the king's health.
King Abdullah underwent a similar operation in October last year and had back surgery twice in the United States in 2010 for a herniated disc, after which he spent three months outside Saudi Arabia recuperating.
Two days after his back operation last year, Abdullah appeared on state television and was released from hospital within five days.
The crown has passed down a line of sons of the kingdom's founder King Abdulaziz Ibn Saud, who died in 1953.
King Abdullah - who took power in 2005 - named his brother Prince Salman, 13 years his junior, heir apparent in June after the death of Crown Prince Nayef bin Abdulaziz.
Salman, who deputises for the king, was shown on television last week meeting visiting U.S. officials. He had chaired two weekly cabinet meetings since the surgery.